In the hot shaping or press hardening of manganese-boron steels and possible composites, such as, for example, TriBond®, tempered tools are used to locally reduce the cooling rate. As a result of the reduced cooling rate, an improved ductility is locally established on the thus treated workpiece. Locally, tool surface temperatures of more than 400° C., preferably between 500° C. and 550° C., are sought. Also light metals, such as aluminum and magnesium, for instance, are shaped in tempered tools at temperatures of more than 150° C. As a rule, electrically operated heating cartridges, which directly deliver their thermal energy into the tool steel, are used for the local tempering of the tools. Consequently, high temperature differences of more than 200° C., can be generated along the surface which run counter to the general interest in a homogeneous warming of the surface. Finally, the different temperatures lead to different cooling rates in the material of the workpiece and thus to different strengths in the finished workpiece. Moreover, it is often, for design reasons, not possible to arrange the heating cartridge such that a desired heat output arrives at a specific place. Furthermore, maintenance works on the tool at regular intervals require that the heating cartridges are exchanged. Since the heating cartridges, however, are inserted with fit into the tool, the high temperatures often give rise to integrally bonded connections between the heating cartridge and the tool, whereby a release of the heating cartridge from the tool is made more difficult.